Chaos–nonchaos phase transitions induced by multiplicative noise in ensembles of coupled two-dimensional oscillators

We study an analytically tractable model of ensembles of mean-field coupled two-dimensional limit-cycle oscillators to investigate the effects of noise on the dynamic behavior in the thermodynamic limit. The two-dimensional limit-cycle oscillator has nonlinearity only in the coupling part, and two kinds of noise, Langevin noise and noise introduced in the coupling strength, which is regarded as multiplicative noise, are dealt with. Under the influence of noise in the coupling strength, phase transitions involving chaos–nonchaos bifurcations are found to occur for an appropriate choice of the nonlinearity as the noise level is changed, while the usual Langevin noise dose not induce such bifurcations in our model.